The following are some web-sites where the Vedas can be read:
1. from http://www.sacred-texts.com/hin/index.htm#vedas
i. Rig Veda
a. The Rig-Veda
translated by Ralph Griffith [1896]
A complete English translation of the Rig Veda.
The complete Rig Veda in Sanskrit, in Unicode Devanagari script and standard romanization.
c. Vedic Hymns, Part I (SBE 32)
Hymns to the Maruts, Rudra, Vâyu and Vâta, tr. by F. Max Müller [1891]
A masterpiece of linguistics and comparative mythology: translations and deep analysis of the Vedic Hymns to the Storm Gods.
d. Vedic Hymns, Part II (SBE 46)
Hymns to Agni, tr. by Hermann Oldenberg [1897]
The Vedic Hymns to Agni.
e. A Vedic Reader for Students (excerpts)
by A.A. Macdonell [1917]
An introduction to the Dramatis Personæ of the Rig Veda.
ii. Sama Veda
translated by Ralph Griffith [1895]
A collection of hymns used by the priests during the Soma sacrifice. Many of these duplicate in part or in whole hymns from the Rig Veda. This is a complete translation.
iii. Yajur Veda
a. The Yajur Veda (Taittiriya Sanhita)
translated by Arthur Berriedale Keith [1914]
A complete translation of the Black Yajur Veda. The Yajur Veda is a detailed manual of the Vedic sacrificial rites.
b. The Texts of the White Yajurveda
translated by Ralph T.H. Griffith [1899]
A complete translation of the White Yajur Veda.
iv. Atharva Veda
The Atharva Veda also contains material from the Rig Veda, but of interest are the numerous incantations and metaphysical texts, which this anthology (part of the Sacred Books of the East series) collects and categorizes. The Atharva Veda was written down much later than the rest of the Vedas, about 200 B.C.; it may have been composed about 1000 B.C.
a. The Hymns of the Atharvaveda
translated by Ralph T.H. Griffith [1895-6]
The unabridged Atharva Veda translation by Ralph Griffith.
translated by Maurice Bloomfield [1897]
(Sacred Books of the East, Vol. 42)
The Sacred Books of the East translation of the Atharva-veda.Selected hymns from the Atharva-veda.
2. from http://www.bharatadesam.com/spiritual/rvs/rv_main_index.php